Question: Solve for $x$ : $6x^2 + 30x + 36 = 0$
Answer: Dividing both sides by $6$ gives: $ x^2 + {5}x + {6} = 0 $ The coefficient on the $x$ term is $5$ and the constant term is $6$ , so we need to find two numbers that add up to $5$ and multiply to $6$ The two numbers $3$ and $2$ satisfy both conditions: $ {3} + {2} = {5} $ $ {3} \times {2} = {6} $ $(x + {3}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x + 2) = 0$ $x + 3 = 0$ or $x + 2 = 0$ Thus, $x = -3$ and $x = -2$ are the solutions.